Please Show Work An analyst estimates that the probability o

Please Show Work

An analyst estimates that the probability of default on a seven-year AA-rated bond is 0.06, while that on a seven-year A-rated bond is 0.13. The probability that they will both default is 0.04.

What is the probability that at least one of the bonds defaults?

What is the probability that neither the seven-year AA-rated bond nor the seven-year A-rated bond defaults?

Given that the seven-year AA-rated bond defaults, what is the probability that the seven-year A-rated bond also defaults?

Solution

Prob (atleast one bond defaults) = 0.06+0.13-0.04 = 0.15

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P(that neither one defaults) 1-0.15 = 0.85

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P(A defaults/AA defaults) = P(Intersection)/P(AA) = 0.04/0.06 = 0.667